The average quantum physicist on the street believes that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian $H=p^2+ix^3$, which is obviously not Dirac Hermitian, has a real positive discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory.

This talk will describe the best current understanding of the interior structure of astronomically realistic black holes.
A common misconception is that matter falling into a black hole simply falls to a central singularity, and that's that.
Reality is much more interesting. Rotating black holes have not only outer horizons, but also inner horizons. Penrose (1968) first pointed out that an infaller falling through the inner horizon would see the outside Universe infinitely blueshifted, and he speculated that this would destabilize the inner horizon.

The gravitational observatory LISA will detect radiation from massive black hole sources at cosmological distances, accurately measure their luminosity distance and help identify the electromagnetic counterparts that such sources may generate. I will describe various astrophysical scenarios for the generation of electromagnetic counterparts and discuss observational strategies aimed at identifying them. Successful identifications will enable novel studies of black hole astrophysics and cosmological physics.

Much work on quantum gravity has focused on short-distance problems such as non-renormalizability and singularities. However, quantization of gravity raises important long-distance issues, which may be more important guides to the conceptual advances required. These include the problems of black hole information and gauge invariant observables, and those of inflationary cosmology. An overview of aspects of these problems, and apparent connections, will be given.

A system of spins with complicated interactions between them can have many possible configurations. Many configurations will be local minima of the energy, and to get from one local minimum to another requires changing the state of very many spins. A system like this is called a spin glass, and at low temperatures tends to get caught for very long times at a local minimum of energy, rather than reaching its true ground state.

The AdS/CFT correspondence relates large-N, planar quantum gauge theories to string theory on the Anti-de-Sitter background. I will discuss exact results in field theories with AdS duals, which can be obtained with the help of diagram resummations, mapping to quantum spin chains and two-dimensional sigma-models.

"Conventional" superconductivity is one of the most dramatic phenomena in condensed matter physics, and yet by the 1970's it was fully understood - a solved problem much like quantum electrodynamics. The discovery of high temperature superconductivity changed all that and opened the door, not only to higher Tc's, but also to a wealth of even more exotic phenomena, including things like topologically ordered superconductors with factional vortices and non-Abelian statistics.

A Majorana fermion is a particle that is its own antiparticle. It has been studied in high energy physics for decades, but has not been definitely observed. In condensed matter physics, Majorana fermions appear as low energy fractionalized quasi-particles with non-Abelian statistics and inherent nonlocality. In this talk I will first discuss recent theoretical proposals of realizing Majorana fermions in solid-state systems, including topological insulators and nanowires. I will next propose experimental setups to detect the existence of Majorana fermions and their striking properties.

In this talk we will explore a "toy model" of quantum theory that is similar to actual quantum theory, but uses scalars drawn from a finite field. The set of possible states of a system is discrete and finite. Our theory does not have a quantitative notion of probability, but only makes the "modal" distinction between possible and impossible measurement results. Despite its very simple structure, our toy model nevertheless includes many of the key phenomena of actual quantum systems: interference, complementarity, entanglement, nonlocality, and the impossibility of cloning.